Philolaus       Article     History   Tree Map
  Encyclopedia of Keywords > Glossaries > Glossary of Ancient Greeks > Philolaus /   Michael Charnine

Keywords and Sections
Review of Short Phrases and Links

    This Review contains major "Philolaus"- related terms, short phrases and links grouped together in the form of Encyclopedia article.


  1. Philolaus was born in either Croton, Tarentum, or Heraclea, according to the doxography of Diogenes Laertius.
  2. Philolaus was the most prominent Pythagorean of the preceding generation (ca.
  3. Philolaus was probably born in Croton (after a Greek historian Diogenes La-rtius) or in Tarentum or Heraclea.
  4. Philolaus was the originator of the former school, whose crowning achievement was the discovery of the heliocentric solar system.
  5. Philolaus was perhaps also connected with the Pythagorean exiles at Phlius mentioned in Plato's Phaedo.


  1. This dating fits Philolaus exactly.
  2. We know very little about Philolaus' life.
  3. Philolaus is unusual in arguing that the embryo is composed of just one element, the hot, and has no cold in it.
  4. They are also shown to be pupils of Socrates, however, and it is unclear that their connection to Philolaus was any closer than their connection to Socrates.
  5. Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher.


  1. Philolaus should not be understood as simply a Pythagorean, however.
  2. In fact, Philolaus noted that one whole note is equal to two half notes plus a Pythagorean comma.


  1. The central fire rather than the sun is at the center of Philolaus' cosmos.
  2. The central evidence for Philolaus' date is Plato's reference to him in the Phaedo (61d-e).
  3. The next stage in Philolaus' cosmogony after the construction of the central fire helps to identify yet more unlimiteds.
  4. The same is true of the astronomical system built around the central fire, which the later tradition assigns to Philolaus and which Aristotle ( Metaph.


  1. Aristotle's testimony is largely confirmed by the content of Philolaus' philosophy.
  2. Philolaus This is a file in the archives of the Stanford Encyclopedia of Philosophy.


  1. Philolaus and Eurytus are listed not under Croton but under Tarentum, just as they are in one of the Fragments of Aristoxenus (Fr.
  2. Diogenes Laertius says that Philolaus was from the Greek city of Croton in southern Italy, but our earliest sources are divided as to his city or origin.


  1. He was taught for a while by Philolaus and he was a teacher of mathematics to Eudoxus of Cnidus.
  2. Retrograde motion was only first addressed almost a century after Philolaus by Eudoxus.

Fifth Century

  1. The other major Pythagoreans of the fifth century were Philolaus and Eurytus, who are discussed above.
  2. In order for Philolaus to have been a prominent teacher by the later fifth century he must have been born no later than 440.
  3. We know from Plato that Philolaus was there towards the close of the fifth century, and Lysis was afterwards the teacher of Epaminondas.

Human Beings

  1. Philolaus posited a strict hierarchy of psychic faculties, which allows him to distinguish human beings from animals and plants.
  2. Like many other Presocratics Philolaus drew an analogy between the birth of the cosmos and the birth of a human being.
  3. Philolaus also presented a medical theory in which there was a clear analogy between the birth of a human being and the birth of the cosmos.


  1. This tradition also suggests that Plato cribbed the Timaeus from Philolaus' book.
  2. Fragments 4 and 5 suggest that Philolaus' program was to discover the numbers and numerical relations that govern the phenomena which we observe, and Fr.


  1. Parmenides is the only Presocratic before Philolaus to emphasize the role of limit in his account of reality.
  2. Philolaus posits limiters and unlimiteds as first principles and emphasizes the role of number in understanding the cosmos.


  1. It is logical to begin with the very first thing that is put together in Philolaus' cosmos.
  2. This scale provides Philolaus' only surviving explicit example of the bonding together of limiters and unlimiteds by a harmony.
  3. Thus, in Philolaus' system the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers.


  1. The earliest such description of a scale is found in Philolaus fr.
  2. We present here a tabulation and diagram of the notes in a reference tetrachord based on the description of divisions of intervals given by Philolaus.


  1. Nicolaus Copernicus mentions in De revolutionibus that Philolaus already knew about the Earth's revolution around a central fire.
  2. According to Nicolaus Copernicus, Philolaus already knew about the Earth's revolution in a circular orbit around the Sun.
  3. But Philolaus the Pythagorean believes that, like the sun and moon, it revolves around the fire in an oblique circle.
  4. Based on data from Nicolaus Copernicus, Philolaus already knew about a Globe's revolution around the round orbit around the Sun.


  1. III 34. 139) reports that Archytas was the pupil of Philolaus, and this is not improbable.
  2. Hippasus). A second tradition reports that Plato bought three books from Philolaus (D. L. III 9; VIII 15 and 84).


  1. The problem is that Aristotle never explicitly describes the Pythagoreanism which he discusses as derived from Philolaus' book.
  2. Second, Philolaus' book seems to have been available to Aristotle's pupil Meno (DK 44 A27-8) and hence is likely to have been available to Aristotle as well.
  3. In Book 3.8, Boethius describes Philolaus's method of dividing small intervals.


  1. The language of this fragment shows that Philolaus is firmly in the tradition of Presocratic philosophy.
  2. Figure 8 shows that Philolaus- diatonic scale consists of two disjunct tetrachords that span the standard Greek -octave- between E-E'.


  1. There is no evidence that Philolaus made any significant contribution in these areas.
  2. Philolaus makes a significant advance over earlier Presocratics by making a firm distinction between thinking and perception.


  1. The story of Plato's purchase of these books from Philolaus was probably invented to authenticate the three forged treatises of Pythagoras.
  2. Philolaus, who was probably two generations later than Hippasus, might have been influenced by Hippasus in starting his cosmology with the central fire (Fr.


  1. Philolaus' genuine book was one of the major sources for Aristotle's account of Pythagorean philosophy.
  2. Burkert sees evidence that Philolaus was not interested in rigorous mathematics in the mathematically nonsensical account of music in Fr.


  1. Starting from the system of Philolaus he developed his own sophisticated account of the world in terms of mathematical proportion.
  2. Philolaus' most significant innovation, however, is to argue that the cosmos cannot be adequately explained in terms of unlimiteds alone.


  1. There has been considerable controversy concerning the 20+ fragments which have been preserved in Philolaus' name.
  2. As in the case of Philolaus' cosmogony, there is considerable controversy about the precise nature of Philolaus' astronomy.


  1. The ancient tradition gives no indication of who Philolaus' teacher(s) might have been.
  2. Some might argue that Aristotle did not know of a book by Philolaus and hence that there was no such book.
  3. Books about "Philolaus" in

Book: Keywen Category Structure

  Short phrases about "Philolaus"
  Originally created: September 10, 2007.
  Please send us comments and questions by this Online Form
  Please click on Move Up to move good phrases up.
0.0068 sec. a=1..